Find the Midpoint (5 square root of 2,7 square root of 3) , ( square root of 2,- square root of 3)

$(5 \sqrt{2}, 7 \sqrt{3})$ , $(\sqrt{2}, - \sqrt{3})$

Step 1

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 2

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{5 \sqrt{2} + \sqrt{2}}{2}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Step 3

Add $5 \sqrt{2}$ and $\sqrt{2}$ .

$(\frac{6 \sqrt{2}}{2}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Step 4

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt{2}$ .

$(\frac{2 (3 \sqrt{2})}{2}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 (3 \sqrt{2})}{2 (1)}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Cancel the common factor.

$(\frac{2 (3 \sqrt{2})}{2 \cdot 1}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Rewrite the expression.

$(\frac{3 \sqrt{2}}{1}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Divide $3 \sqrt{2}$ by $1$ .

$(3 \sqrt{2}, \frac{7 \sqrt{3} - \sqrt{3}}{2})$

Step 5

Subtract $\sqrt{3}$ from $7 \sqrt{3}$ .

$(3 \sqrt{2}, \frac{6 \sqrt{3}}{2})$

Step 6

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt{3}$ .

$(3 \sqrt{2}, \frac{2 (3 \sqrt{3})}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(3 \sqrt{2}, \frac{2 (3 \sqrt{3})}{2 (1)})$

Cancel the common factor.

$(3 \sqrt{2}, \frac{2 (3 \sqrt{3})}{2 \cdot 1})$

Rewrite the expression.

$(3 \sqrt{2}, \frac{3 \sqrt{3}}{1})$

Divide $3 \sqrt{3}$ by $1$ .

$(3 \sqrt{2}, 3 \sqrt{3})$

Step 7